Question

A solid block is attached to a spring scale. When the block is suspended in air, the scale reads 21.4 N ; when it is completely immersed in water, the scale reads 15.2 N .
a)What is the volume of the block?
b)What is the density of the block?

Answer 1

Answer on Question #75819, Physics / Mechanics — Relativity

Question A solid block is attached to a spring scale. When the block is suspended in air, the scale reads 21.4 N ; when it is completely immersed in water, the scale reads 15.2 N . a)What is the volume of the block? b)What is the density of the block?

Solution The forces in these cases (air and water) are:

$F_{a}=mg=\rho_{b}Vg$

$F_{w}=(\rho_{b}-\rho_{w})Vg$

where $\rho_{w}=1000$ kg/m^{3} is density of water and $\rho_{b}$ is density of the block and $V$ is its density. We can find it from this two equations:

$\frac{F_{a}}{F_{w}}=\frac{\rho_{b}}{(\rho_{b}-\rho_{w})}$

$\rho_{b}=\rho_{w}\frac{F_{a}}{F_{a}-F_{w}})=1000\cdot(1\frac{21.4}{21.4-15.2})\approx 3452\,kg/m^{3}$